If it has no mint mark or a letter P, it's minted in Philadelphia. If it has a D, it's from Denver.
The last silver quarters were minted in 1964.
For the year 1853 most all Quarter Eagles were struck at the Philadelphia mint, so they have no mintmark. A few were made at the Denver mint and will have a "D" mintmark.
If you mean a US Cent, there is a 'D' below the date if it was minted in Denver, Colorado, an 'S' if it was minted in San Francisco, California. If neither of these mintmarks is there, it is from Philladelphia, Pennsylvania.
Simple, no quarters have ever been made in Delaware, the "D" mintmark means it was made in Denver.
If it's a US quarter minted in 1965 or later, it's not silver (there are silver coins minted in "proof sets", but these came in a special labeled display case; you're not going to find one in pocket change). US quarters minted in 1964 or before were partly (about 90%, I think) silver.
If you have a Denver minted coin it will have the mintmark D. The location of the mintmark will depend on the date.
It's the year that the coin was minted. If you look under the date you can tell where it was minted, too: "D" = Denver Mint "S" = San Francisco No letter = Philadelphia
US coins dated 1965-1967 don't carry mint marks, so it's not possible to tell where your quarter was minted. In circulated condition it has no added value -- there is no silver in it. A nice uncirculated one is worth about 50 cents.
On the back of the coin under the "O" in "ONE" there should either be no mark, a D or an S. If your coin has no mark, it was minted in Philadelphia. If it has a D it was made in Denver and if it has an S it was made in San Fransisco.
You can tell if a dime or quarter is silver by checking the year minted. Dimes minted before 1965 and quarters minted before 1964 are made of 90% silver. You can also conduct a magnet test - if the coin is attracted to a magnet, it is not silver.
In the US, there will be a mint mark on the coin if it was minted in Denver or San Francisco (the letter D or S respectively). If there is no mint mark, it was minted in Philadelphia. The exception to this is that coins minted from 1965-67 don't have mint marks even if they were minted outside of Philadelphia, so for those years you can't really tell.